Substituting 1 for x in the equation 5x + 3=x⋅5 + 3 is a test case for which property?(1 point)
Responses
The Associative Property of Multiplication
The Commutative Property of Addition
The Associative Property of Addition
The Commutative Property of Multiplication
The Commutative Property of Addition
Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a.
Step 1: [missing]
Step 2: 10+13a=10+13a
Step 3: The expressions are equivalent because they both equal the same value.
(1 point)
Responses
10+12a+a=10+13a
d plus 10 plus a equals 10 plus a plus d
12a+10=10+12a
d plus 10 plus a equals 10 plus a plus d
12a+10+a−10=10+a+12a−10
d plus 10 plus a equals 10 plus a plus d
12a+10+a−a=10+a+12a−a
Step 1: 12a+10+a=10+a+12a (Commutative Property of Addition)
Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a.
Step 1: [missing]
Step 2: 10+13a=10+13a
Step 3: The expressions are equivalent because they both equal the same value.
(1 point)
Responses
10+12a+a=10+13a
12a+10=10+12a
12a+10+a−10=10+a+12a−10
12a+10+a−a=10+a+12a−a
Step 1: 12a+10+a = a+10+12a (Commutative Property of Addition)
The correct answer is the Commutative Property of Addition. When we substitute 1 for x in the equation 5x + 3 = x⋅5 + 3, it becomes 5(1) + 3 = 1⋅5 + 3. According to the Commutative Property of Addition, the order of addition does not matter.
To determine which property is being tested, we need to substitute the value of 1 for x in the equation 5x + 3 = x⋅5 + 3.
Step 1: Substitute x = 1 into the equation:
5(1) + 3 = 1⋅5 + 3
Step 2: Simplify both sides of the equation:
5 + 3 = 5 + 3
Step 3: Perform the addition on both sides:
8 = 8
In this case, we can see that both sides of the equation are equal, so the equation remains true regardless of the value of x. This suggests that the property being tested is the Commutative Property of Addition.
Therefore, the correct answer is:
- The Commutative Property of Addition.